Evaluate the following integral in spherical coordinates. SSS--(=y2 +22)3120v 3/2 dV; D is a ball of...
3. Use spherical coordinates to evaluate the integral V dV where is the portion of the unit ball srº + y2 + 22 S 1 in the first octant.
Evaluate the following integral. SSS (xy + x2 + y2) dV; D = {(x,y,z): -55x55, -15ys1, -35253} D SS Scy (xy + x2 + yz) DV = (Simplify your answer.) D
dV, where is the unit ball in R3, that is, Use spherical coordinates to compute the integral We E = {(x, y, z)| 22 + y2 + 2 <1}.
5. In spherical coordinates evaluate the triple integral [ff (x2 + y2 +z?)2dV where D is the unit ball. (20 points)
4. Using spherical coordinates, evaluate the triple integral: ry: dl, where E lies between the spheres r2+94:2-4 and r2+92+ะ2-16 and above the cone V+v) or Recommend separating! 5. Using spherical coordinates, find the volume of the solid that lies within the sphere r2+y2+2 9, above the ry-plane, and below the cone ะ-V/r2 + y2 Reconnnend separating! 6. Using spherical coordinates, evaluate the triple integral: 2 + dV where E is the portion of the solid ball 2+2+2 s 4 that...
(1 point) Use spherical coordinates to evaluate the triple integral dV, e-(x+y+z) E Vx2 + y2 + z2 where E is the region bounded by the spheres x² + y2 + z2 = 4 and x² + y2 + z2 16. Answer =
Evaluate the following integral in cylindrical coordinates. 6 213 16x2 SS S -x2 - y2 dy dx dz e 0 0 X 6 213 16-X2 S ,-x2 - y2 dy dx dz = 0 0 x (Simplify your answer. Type an exact answer, using a as needed.)
Suppose you have to use spherical coordinates to evaluate the triple integral SI z dV where D is the solid region that lies inside the cone z = 22 + y2 and inside the sphere 22 + y2 +22 = 144 D Then the triple ingral in terms of spherical coordinates is given by Select all that apply p3 cos • sin o dp do do D [!] > av = 6*6** ? [!] > av = 6"* )*S" So*%*%**...
Use spherical coordinates. Evaluate (4 − x2 − y2) dV, where H is the solid hemisphere x2 + y2 + z2 ≤ 16, z ≥ 0. H
Evaluate the integral below by changing to spherical coordinates. -y2 100 100 10 -10 -x2-y -y2 100 100- Evaluate the integral below by changing to spherical coordinates. -y2 100 100 10 -10 -x2-y -y2 100 100-